Shortly after posting about my day in Sheffield, I received an email from a reader who actually studies in the city, which quite clearly puts my report to shame! Here's a more detailed insight into the bus scene there, complimented by a few photographs of mine.
"In response to your Sheffield bus scene, you missed a huge amount out. I am used to the Norwich bus scene, but moving up here for university, I’ve learnt a lot about the Sheffield bus scene too. I understand that you couldn't find a bus station (here in Yorkshire they're called Interchanges). The interchanges up here are pretty much the same as Castle Meadow, St Stephens and Theatre Street. By the look of your flickr photos, had you walked around the other side of Sheffield Hallam University, you would have met the Sheffield Interchange.
Anyway, regarding FirstSheffield, you're right about the Geminis being common up here. However so too are Presidents (not to the same extent as Norwich), and a small fleet of Enviro 400s, commonly operating the 51 line. As for the single-deckers, there's quite a big fleet of new StreetLites here in Sheffield. Additionally, the Eclipses are common. The Renowns though? These buses are often used on a couple of routes or during peak hours. Considering the new First livery, pretty much all the buses here are in the new design, just a few Renowns and ALX400s remain in the barbie livery. They're not bothering with repainting those as either the buses will be scrapped, or repainted into training liveries for other regions. One notable bus is the B7L Eclipse Y661 UKU (60703), its an Eclipse at the front, then a Renown at the back. First time I saw it, I thought I was seeing things.

As for Stagecoach, they have a big affair with the Enviro bus series. Plenty of 300s and 400s. Interestingly, Stagecoach have been running the Enviro 400H, the hybrid model, for a number of years on their Sheffield's flagship 120 route, shared between First and Stagecoach alike. There's even a few darts about, mainly used during the peak hours though. Stagecoach as you say, also run the tram services into Sheffield, 3 lines in total (from Halfway, Hillsborough and Meadowhall)
As for independents, TM Travel are pretty big considering their position as an independent. They tend to operate a large fleet of Optare Solos, with a small number of Versas too. Their entire double-decker fleet is made up of Olympians.
As for other operators, they are running one or two routes, often shared with their bigger rivals. For example, the 272 route (Castleton - Sheffield) is operated by First, TM Travel and Hulleys of Baslow (though I've never seen Hulleys running it, and only seen a TM Travel bus on it once). Sheffield Community Transport (SCT) run around 10 routes, while there are a number of even smaller independents operating the one route.
The route sharing is common place here in Sheffield; the result of the bus partnership that's been set up. You can rarely get each companies' bus maps, there's just an entire sheffield bus map, certainly not the easiest thing to read. In addition the ‘X...’ services (X13, X78 etc.) are in no way ‘express’ or speedy. They are just the same as any other route, stopping at every stop."
A big thanks to Quintin for sending that fantastic report.